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# Fatigue analysis Guide

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```A Guide to Fatigue
Analysis
This guide starts from the applications of fatigue analysis and its
role in FEA simulation. Fundamental concepts and principles will
be introduced such as what is fatigue, fatigue design philosophy,
life estimation methods, stress life approach, etc…
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Page 2
1- What is Fatigue Failure?
Fatigue failure is defined as the tendency of a material to fracture
by means of progressive brittle cracking under repeated
alternating or cyclic stresses of an intensity considerably below the
normal strength.
Although the fracture is of a brittle type, it may take some time to
propagate, depending on both the intensity and frequency of the
stress cycles.
Examples of fatigue failure
All structures and mechanical components that are cyclically
Fundamental requirements during design and manufacturing to
avoid fatigue failure are different for each different case and
should be considered during the design phase.
Page 2
2- Fatigue Design Philosophy
Before attempting to carry out a fatigue calculation, or even
choosing a way of calculating, it is necessary in critical situations
to decide on a design philosophy.
The three main approaches are Safe-Life, Fail-Safe and DamageTolerant.
Safe-Life
Products are designed to survive a specific design
life. Full scale tests are usually carried out with
margins of safety applied. Fairly optimized structures.
A “safe-life” stool.
Any less than three legs and it would fall over!
Fail-Safe
Products are designed to avoid any failure regardless of
costs. If the structure were to fail in some part, it would
capable to working properly, until necessary repairs
A “Fail-Safe” stool.
Failure of one leg would not result in overall failure.
Damage-Tolerant
Products are design to take into account inspection
criterion to investigate the structure periodically to see
whether or not crack have started.
A “damage-tolerant” stool.
The stool has some built in redundancy and is inspected
regularly.
3- Life Estimation Methods
Fatigue analysis itself usually refers to one of two methodologies.
The stress-life (or S-N method), is commonly referred to as the
total life method since it makes no distinction between initiating or
growing a crack. This was the first fatigue analysis method to be
developed over 100 years ago.
The local-strain or strain-life (E-N) method, commonly referred to
as the crack initiation method, was more recently developed and
is intended to describe only the ‘initiation’ of a crack.
Total Life
Crack Initiation
Crack Growth
An idealization of the fatigue design process
Fracture specifically describe the growth or propagation of a
crack once it has been initiated and has given rise to many socalled crack growth methodologies.
Some load histories may be simple and repetitive, while in other
cases they may be completely random. They can also have
constant or variable amplitudes.
material fatigue behavior/properties for fatigue design.
Some real life load histories can occasionally be modeled with
constant amplitude as well.
Sa
time
Stress
Tension (+)
b)
Cycle – 2 reversals
Smax
Sm
Sr
Smin – minimum stress
Smax – maximum stress
Sa – alternating stress (stress amplitude)
Sm – mean stress
Sr – stress range
Sa
Sr
Smin
time
(-)
Stress
(-) Compression
Tension (+)
a)
R – stress ratio
R = -1
R=0
fully reversed cycle
pulsating tension
Examples of stress cycles, (a) fully reversed, and (b) offset.
Stresses can be replaced with load, moment, torque, strain, deflection or stress intensity factors.
5 - Wőhler’s Curve, S-N Curve
This curve has been developed by German August Wőhler for his
systematic fatigue tests done in the 1870’s.
S-N Curve plots the diagram of amplitude of nominal stress as a
function of number of cycles to failure for un-notched (smooth)
specimens.
Mathematical description of the material S-N curve:
A
Sa= σa= A&middot;Nf-B
B
σa – applied alternating stress
A – constant, value of σa at one cycle
B – Basquin’s exponent, slope of the log-log curve
Nf - the number of cycles of stress that a specimen sustains before failure occurs
6 - Stress Life Approach
Stress life method, more commonly known as the S-N or Nominal
Stress method is used for total life calculation.
It assumes the structure to be fully elastic (even in local fatigue
related details like notches). Initiation or growing phase of a crack
is not considered. Applicable to high cycle fatigue problems (low
load-long life). This approach should not be used to estimate
fatigue lives below 10,000 cycles.
Some basic features related to Stress-Life approach:
&middot; Material and component S-N curves
&middot; Stress concentration factors,
&middot; Miner’s cumulative damage theory
&middot; Goodman or Gerber mean stress correction
&middot; Rainflow Cycles Counting
Rainflow cycles counting example
Gerber-Goodman diagram
7 - Strain Life Approach
This method is also called Critical Location (CLA) approach, Local
Stress-Strain, E-N or Crack Initiation.
It applies when the structure durability depends on stress
amplitude of local strain at the crack initiation place. Strain-life
design method is based on relating the fatigue life of notched parts
to the life of small unnotched specimens cycled to the same
strains as the material at the notch root.
This approach is best suited for low cycle fatigue problems,
where the applied stresses have a significant plastic component.
ΔS
Δε
Critical zone
Smooth specimen
Δε
ΔS
Notch
The concept of similitude between strain controlled
test specimen and a component being designed
8 - Strain Life Curve
E-N curve shows the relationship between the strain and the
number of cycles causing fatigue failure as expressed in
equation below.
By applying a number of individual strain amplitudes to the
E-N curve, which have been extracted through rainflow-counting,
each number of cycles and the corresponding individual damage
level are obtained.
Δε/2 – total strain amplitude = εa
Nf - the number of cycles of stress that a
specimen sustains before failure occurs
E – modulus of elasticity
σf’ – fatigue strength coefficient
εf’ – fatigue ductility coefficient
C – fatigue ductility exponent
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